Non-reversible Markov chain Monte Carlo methods often outperform their reversible counterparts in terms of asymptotic variance of ergodic averages and mixing properties. Lifting the state-space (Chen et al., 1999; Diaconis et al., 2000) is a generic technique for constructing such samplers. The idea is to think of the random variables we want to generate as position variables and to associate to them direction variables so as to design Markov chains which do not have the diffusive behaviour often exhibited by reversible schemes. In this paper, we explore the benefits of using such ideas in the context of Bayesian model choice for nested models, a class of models for which the model indicator variable is an ordinal random variable. By lifting this model indicator variable, we obtain non-reversible jump algorithms, a non-reversible version of the popular reversible jump algorithms introduced by Green (1995). This simple algorithmic modification provides samplers which can empirically outperform their reversible counterparts at no extra computational cost. The code to reproduce all experiments is available online.

中文翻译：

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贝叶斯嵌套模型选择的不可逆跳转算法

不可逆马尔可夫链蒙特卡罗方法在遍历平均值的渐近方差和混合属性方面通常优于其可逆对应方法。提升状态空间（Chen 等人，1999 年；Diaconis 等人，2000 年）是构建此类采样器的通用技术。这个想法是将我们想要生成的随机变量视为位置变量并将方向变量与它们相关联，从而设计出不具有可逆方案通常表现出的扩散行为的马尔可夫链。在本文中，我们探讨了在贝叶斯模型选择嵌套模型的背景下使用这些想法的好处，嵌套模型是一类模型指示变量是有序随机变量的模型。通过提升这个模型指标变量，我们得到不可逆跳跃算法，Green (1995) 引入的流行可逆跳跃算法的不可逆版本。这种简单的算法修改提供的采样器可以在没有额外计算成本的情况下凭经验超越其可逆对应物。重现所有实验的代码可在线获得。